This specification relates to squaring binary finite field elements. Binary finite field arithmetic operations are used in elliptic curve cryptography systems and other applications. For example, a coordinate of an elliptic curve point can be represented as a binary finite field element, and binary finite field arithmetic can be used to perform calculations based on the coordinates. Embedded hardware devices are often used to perform intensive binary finite field operations, such as multiplication, squaring, and inversion. Some embedded hardware devices perform binary squaring in a single cycle.
Like reference numbers and designations in the various drawings indicate like elements.